Euro-Atlantic system, and especially the relationship between the US and the European Union and NATO cooperation with the EU, despite the difficulties, are and will be one of the most important elements in the process of building a new global multipolar order. However, the United States and the European Union should pursue a more correlated international policy, based on a realistic and idealistic vision of the world. The world needs the Euro-Atlantic community, as there is no and there won't be in the near future such integrated community of values and interests in the new emerging global order. The above problems are describe in this monograph, which was written in the framework of the research project called: "The role of the Euro-Atlantic system in a multipolar world in the context of the emerging new global order."